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Seminar by Suchismita Tarafdar on July 12

Title: Generalized Envelope Theorems: Applications to Dynamic Programming

Speaker: Suchismita Tarafdar, Shiv Nadar University

Time and Date: 11:00 am, Tuesday July 12, 2016

Venue: LC 102

Abstract:
We show in this paper that Lipschitz functions provide a suitable framework for the generalization of classical envelope theorems to a broad class of constrained programs relevant to economic models where nonconvexities play a key role and where primitive data may not be constinuously differentiable. We give sufficient conditions for the value function of a Lipschitz program to inherit the Lipschitz property, and then obtain bounds for the upper and lower directional Dini derivatives of the value function. We next strengthen our asssumptions to derive sufficient conditions for the directional differentiability, differentiability, and smoothness of the value function, thus obtaining a collection of generalized envelope theorems encompassing many existing results in the literature.

Some of our findings are then applied to decision models with discrete choices, to dynamic programming with and without concavity, as well as to the problem of existence and characterization of Markov equilibrium in in dynamic economies with nonconvexities.